A fair n-sided die is rolled n times. Assuming the rolls are independent, calculate the probability of getting a match on roll i, i.e. on roll i the die shows i.
I don’t think you have posted what you are really asking.
Suppose we roll an ordinary die six times.
The probability of getting a 1 on the first roll is .
The probability of getting a 2 on the second roll is .
…
The probability of getting a 6 on the sixth roll is .
Now is that truly what you asked?
Yes i understand that the likelihood of a matct is 1/n on any particular trial.
But i dont understand how to calulate the probability of getting a match on roll i.
Where does n start and where does it end?
If its infinite then isnt the probabilty of getting a match 1?
Perhaps you mean what is the probability of getting at least one match?
If so, this is 1 - P(no match). The probability of not getting a match on the nth roll is , so assuming the rolls are independent, the probability of no macth in n rolls is , and
.
If you are interested in large n,
.